Concept

Transient

The early part of an orbit, before it has settled onto whatever it settles onto. Discarding it is what makes a bifurcation diagram legible, and how long it lasts is a separate question from where it ends up.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

the logistic map at 3.2, iterated from 0.2. A map drawn as a curve with the diagonal across it, and the staircase that iterating it produces.

The staircase that shows the whole orbit

Take a number, feed it to a rule, feed the answer back in. There is a way of drawing that on the rule's own graph which turns the entire future of a starting point into a shape — and the shape is legible.

dynamics · iteration

The logistic map's bifurcation diagram, 2.4 to 4. For each parameter, the values the orbit settles into, plotted as a column of points.

The road paved with doublings

Turn one dial slowly and watch what a map settles into. It settles on a point, then on two points, then four, then eight — faster and faster, and the doublings run out at a parameter that is finite.

dynamics · period doubling

Named alongside it

The objects these essays reach for when they reach for this one.

Attractor Logistic map Periodic orbit Self similarity Bifurcation Chaos Cobweb Fixed point Iteration Orbit Period doubling Stability

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